Compared to our closest primate relatives, human life history involves greater longevity, which includes a distinctive postmenopausal life stage. Given mammalian reproductive physiology in which females build a finite stock of cells that can become oocytes early in life, which then continuously deplete mostly through cell death while males produce new sperm throughout adulthood, the postmenopausal stage makes the sex ratio in the fertile pool, called the adult sex ratio (ASR), male biased. Additionally, this affects a more fine-grained ratio, the operational sex ratio (OSR), defined as the ratio of males to females currently able to conceive. Here, we construct an ODE model in which males compete for paternities using either a multiple-mating or mate-guarding strategy. Our focus is on investigating the differences of strategy choice between populations with varying life histories, which include a distinct post-fertile stage for adult females. By simulating the system, we determine the dominant strategy and its dependence on various parameter combinations. Our results show that an increase in OSR and ASR correlates well with a change in the dominant strategy from multiple mating to guarding.